Approches formelles en syntaxe et sémantique

1. Approches formelles en syntaxe et sémantique Alain Lecomte UMR 7023 Structures Formelles de la Langue

2. programme minimaliste • Deux opérations générales: • merge • move

3. definition • A minimalist grammar is a 4-tuple (V, Cat, Lex, F) where: • V = P  I • Cat = (base  select  licensee  licensor), • Lex = cf. above • F = {merge, move} • ex: P = {/marie/, /pierre/, /le/,/quechua/,…} I = {(marie), (pierre), (quechua), (le),…} • base = {c, t, v, d, n, …} • select = { =x ; xbase} • licensee = { -k, -wh, …} • licensor = {+k, +K, +wh, +WH, …}

4. merge • A pair of trees ,  belongs to the domain of merge iff  has the feature =x and  has the feature x for some xbase. • merge(, ) = [< ’, ’ ] if  has only one node • merge(, ) = [> ’, ’ ] if  has more than one node • ’ :  - {=x} and ’ :  - {x} •  « has the feature f » : the first element of the sequence which labels  ‘s head is f

5. projections, heads… • When two constituants are merged, one of them « projects over » the other, we write: x < y for « x projects over y » • x is head of y if: • y leaf and x = y • or : x is head of some z which projects over all its sisters

6. move •  belongs to the domain of move iff  has the feature +y and  has exactly one maximal subtree 0 which has the feature –y • move() = [> ’0 , ’] • where ’0 is 0 – {-y} and ’is  - {+y} and ’0 is replaced by a featureless node if y is strong and with only the phonetic features if it is weak. • maximal : his root is the maximal projection of some head

7. Example (Stabler 97) Lexicon: d –k maria d –k quechua =n d –k some =n d –k every n student n language =d +k =d v speaks =c +k =d v believes =v +K t =t c =t c -k

8. Merge =n d –k every n language

9. < d –k every language

10. < =d +k =d v speaks d –k every language

11. < < +k =d v speaks –k every language

12. < –k every language Move < +k =d v speaks

13. < –k every language Move < < +k =d v speaks –k every language

14. > < every language Move < l =d v speaks

15. > < (every) (language) < =d v speaks /every//language/ LF : (some linguist)(every language)(speaks) PF: /some linguist speaks every language/

16. merge • {Peter} {smoke} (sans tenir compte du temps) n /peter/ =n v /smoke/

17. merge • {Peter} {smoke} /peter/ v /smoke/

18. merge • {Peter} {smoke} • Type driven interpretation t /peter/ e v /smoke/ e  t

19. merge • {Peter} {smoke} (without tense) • Type driven interpretation t smoke(p*) /peter/ e v /smoke/ e  t x. smoke(x) p*

20. Merge principle • Two expressions can merge only if their semantical types allow it : • If  and  are expressions, if  has the type of a function the domain of which contains , then they can merge and the resulting expression  is such that: [[]] = [[]]([[]]) (with the resulting type)

21. move • personne que Pierre admire N N CP personne que C’ C IP Pierre admire t

22. move • personne que Pierre admire : • x. [personne(x)admire(pierre, x)] • Hypothesis (Heim & Kratzer): • every trace translates into an e-type variable (if an NP is moved) • Pierre admire t : • admire(pierre, xn)

23. move • personne que Pierre admire N N CP P.x. [P(x)admire(pierre, x)] personne que C’ C IP admire(pierre, x) Pierre admire t

24. move • personne que Pierre admire N N CP P.x. [P(x)admire(pierre, x)] personne que C’ U. P.x. [P(x)U(x)] C IP admire(pierre, x) Pierre admire t

25. move • personne que Pierre admire N N CP P.x. [P(x)admire(pierre, x)] personne ? que C’ U. P.x. [P(x)U(x)] C IP admire(pierre, x) Pierre admire t

26. types N <e, t> N CP P.x. [P(x)admire(pierre, x)] personne t que C’ U. P.x. [P(x)U(x)] <<e, t>, <<e, t>, <e, t>>> C IP admire(pierre, x) Pierre admire t

27. types N <e, t> N CP P.x. [P(x)admire(pierre, x)] personne mismatch t que C’ U. P.x. [P(x)U(x)] <<e, t>, <<e, t>, <e, t>>> C IP admire(pierre, x) Pierre admire t

28. N <e, t> N CP P.x. [P(x)admire(pierre, x)] personne que U. P.x. [P(x)U(x)] <<e, t>, <<e, t>, <e, t>>> types <e, t> Abstraction step t C’ C IP admire(pierre, x) Pierre admire t

29. N <e, t> N CP P.x. [P(x)admire(pierre, x)] personne que U. P.x. [P(x)U(x)] <<e, t>, <<e, t>, <e, t>>> types <e, t> x. admire(pierre, x) t C’ C IP admire(pierre, x) Pierre admire t

30. Move principle • Let [+f] a tree which has the feature +f, and which contains only one maximal subtree [-f]*, therefore of semantics [[(x)]], where x is a variable representing . Let  the tree obtained by moving  out of , then: • [[]] = [[]](x. [[(x)]][x/x]), if there is no further expected move of . • If there are expected moves of  (other licensees –f in it), • [[]] = (x. [[(x)]][x/x])(y) where y is a fresh variable

31. example • Quel bus tu prends? • Lexicon: • bus : n /bus/ x.bus(x) • quel : =n d –wh /quel/ P.Q.[quel x P(x)Q(x)] • tu : d /tu/ tu • prends : =d =d v /prends/ x.y.monte-dans(y, x) • =v t • =t +WH c

32. n /bus/ x.bus(x) • =n d –wh /quel/ P.Q.[quel x P(x)Q(x)]

33. < /bus/ x.bus(x) • d –wh /quel/ P.Q.[quel x P(x)Q(x)] merge

34. Q.[quel x bus(x)Q(x)] < /bus/ • d –wh /quel/ merge

35. d -wh /quel//bus/ xbus, =d =d v /prends/ x.y.monte-dans(y, x) merge

36. y.monte-dans(y, xbus) < -wh /quel//bus/ =d v /prends/ merge

37. > y.monte-dans(y, xbus) < • d /tu/ tu -wh /quel//bus/ =d v /prends/ merge

38. monte-dans(tu, xbus) > < • /tu/ -wh /quel//bus/ v /prends/ merge

39. monte-dans(tu, xbus) < =v t > < • /tu/ -wh /quel//bus/ v /prends/ merge

40. monte-dans(tu, xbus) < > t < • /tu/ -wh /quel//bus/ /prends/ merge

41. monte-dans(tu, xbus) < < =t +WH c > t < • /tu/ -wh /quel//bus/ /prends/ merge

42. monte-dans(tu, xbus) < < +WH c > < • /tu/ -wh /quel//bus/ /prends/ merge

43. > monte-dans(tu, xbus) < -wh /quel//bus/ < +WH c > < • /tu/ /prends/  move

44. > monte-dans(tu, xbus) < /quel//bus/ < c > < • /tu/ /prends/  move

45. > /quel//bus/ u. monte-dans(tu, u) • Q.[quel x bus(x)Q(x)] < < c > < • /tu/ /prends/  move

46. > /quel//bus/ • [quel x bus(x) monte-dans(tu, x)] < < c > < • /tu/ /prends/  move

47. conclusion • Syntax and semantic cooperate : • merge and move drive semantical operations (application and abstraction) • semantical typing selects the correct derivations (« objects » go to accusatives, « subjects » to nominatives) • Similarities with type-logical grammars : • resource consumption logic • Curry-Howard homomorphism

48. Passive voice • seen :: =d v <e, t> x. seen(x) • was :: =v +NOM infl <t, t> • Paul :: d –k(<<e, t>, t>  e) • Mary :: d -k • by :: =d +obl V= v <e, <<e, t>, <e, t>>> z.u.y.agent(u(y), z)

49. seen :: =d v <e, t>x. seen(x) • was :: =v +NOM infl <t, t> • Paul :: d –k(<<e, t>, t>  e) • Mary :: d -k • by :: =d +obl V= V <e, <<e, t>, <e, t>>> z.u.y.agent(u(y), z) =d v <e, t> d –k e /seen/

50. seen :: =d v <e, t>x. seen(x) • was :: =v +NOM infl <t, t> • Paul :: d –k(<<e, t>, t>  t) • Mary :: d -k • by :: =d +obl V= V <e, <<e, t>, <e, t>>> z.u.y.agent(u(y), z) seen(x) v <e, t> –k e /seen/